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Suppose that p is the smallest prime that divides |G|. Show that anysubgroup of index p in G is normal in G.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Suppose that p is the smallest prime that divides |G|. Show that any
subgroup of index p in G is normal in G.

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